$3.(10$ points$)$ Consider a relation parent $($X$,$ Y$)$ which means $\text{'}$X$\text{'}$ is a parent of $\text{'}$Y$\text{'}.$

$($a$)(5$ points$)$ Write all the facts $($tuples$)$ that describe the following tree$$

$($b$)(5$ points$)$ Consider the following rules for defining ancestor$($X$,$Y$)$:$$

$$ X is an ancestor of Y if X is a parent of Y$.$

$$ X is an ancestor of Y if X is a parent of some Z$,$ and Z is an ancestor of Y$.$

Write a datalog program and apply it to find all ancestors of all nodes in the above tree.